100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
Vector Algebra Questions and Answers $20.89   Add to cart
Quickly navigate to
Preview
  2.  
  3. The University Of Edinburgh (ED)
  4.  
  5. MATHEMATICS VECTORS

Exam (elaborations)

Vector Algebra Questions and Answers
 3 views  0 purchase
  • Course
  • MATHEMATICS VECTORS
  • Institution
  • The University Of Edinburgh (ED)

Vector Algebra Questions and Answers

Preview 2 out of 11  pages

Document information

  • April 6, 2024
  • 11
  • 2023/2024
  • Exam (elaborations)
  • Questions & answers

Subjects

  • vector algebra
  • maths vectoralgebra
  • vector algebra questions and answers

Written for

  • The University of Edinburgh (ED)
  • Unknown
  • MATHEMATICS VECTORS
All documents for this subject (7)

Seller

avatar-seller
UpperCrust

Reviews received

Content preview

VECTOR PRODUCT OF FOUR VECTORS JEE MAINS - VOL - I

VECTOR TRIPLE PRODUCT AND PRODUCT OF FOUR VECTORS

SYNOPSIS a .b a .d
 (a  c ).b  d  
 Vector triple Product : c .b c .d
The vector product of a  b and c is a vector 2 2 2 2

triple Product of three vectors a, b and c . It is
  a  b  . a  b   a  b  a b   a .b 
 Vector Product of Four Vectors :
denoted by a  b  c
a  b  (c  d ) is a vector product of four
 (a  b )  c  (a .c )b  (b .c )a . This is a vector vectors.
in the plane of a and b .
 a b c  d    a b d  c   a b c  d
 a   b  c    a .c  b   a .b  c . This is a vector
  c d a  b   c d b  a
in the plane of b , c
  a b c  d  b c d  a   c a d  b   a b d  c
 (a  b )  c  c  (a  b )
2
 a , b , c are non-zero vectors and   a  b b  c c  a    a b c 

( a  b )  c  a  (b  c )  a & c are collinear  If a , b , c are non coplanar vectors,
(Parallel) (or) ( a  c )  b  0 i.e.,  a b c   0 then any vector r in space can
 Vector triple product is not associative. If a , b , c be expressed as a linear combination ofa , b , c
are non-zero, non-orthogonal vectors., then
 r b c   r c a  b   r a b  c
(a  b )  c  a  (b  c ) . r  a 
i.e.,  a b c   a b c   a b c 
 a  (b  c )  b   c  a   c  (a  b )  0
i.e., in the form r  xa  yb  zc
 a  (b  c ), b  (c  a ), c  (a  b ) are coplanar
i   j  k   j  k  i   k  i  j   0
 If a , b , c and d are coplanar then

 i  a  i   j  a  i   k  a  k   2a
a  b   c  d   0
where a is any vector  If a , b , c and d are parallel vectors (or) collinear

 a  (b  c )  b  ( c  a )  ( a  b )  c vectors, then (a  b )  c  d   0
 To find the direction of a line with greatest slope:
 [a  b b  c c  a ]  [a b c ]2
 Scalar Product of Four Vectors : Let  1 ,  2 be two planes intersecting in a line l1
then the line of greatest slope in 1 is the line lying
( a  b ).(c  d ) is a scalar product of four vectors.
in the plane 1 and perpendicular to the line l1 .
It is a dot product of the vectors a  b and c  d .
Note: Let a , b be the vectors along the normals to the
 (a  b ).(c  d )  a .c  (b .d )  a .d  (b .c )
planes 1 and  2 respectively then the vector
a .c a .d

b .c b .d
 
a  a  b will be along the line of greatest slope
in 1 .

108

, JEE MAINS - VOL - I VECTOR PRODUCT OF FOUR VECTORS

W.E-1: Let a  2 i  j  k , b  i  2 j  k and a 1) 1 2) 0 3) -1 4) 2
unit vector c be coplanar. If c is 3. a  2 i  3 j  4k , b  i  j  k ,
perpendicular to a , then c is equal to
c  4 i  2 j  3k then a   b  c  
a  a  b  (EAM-

Sol: Required unit vector is a  a  b
  2000)
1) 10 2) 1 3) 2 4) 5
a   a  b    a .b  a   a .a  b  9 j  9k
4. a  b  c   b   c  a   c   a  b  
1
c  
2
 j  k  1) 0 2) 0 3) 1 4)  a  b  .c

W.E-2: Let a  i  j and b  2 i  k then point of 5. (a  b )  c  a  (b  c ) if and only if
intersection of the line 1) (a  c )  b  0 2) a  (c  b )  0
r  a  b  a and r  b  a  b is 3) c  (b  a )  0 4)  a b c   1
Sol: We have r  a  b  a   r  b   a  0 6. The vector (a  b )  c is perpendicular to

 r  b  a  r  b  a 1) c 2) a  b 3) both 1 and 2 4) b , c
 r  b  a 7. i  (a  i )  j  (a  j )  k  (a  k ) 
Similarly, the equation of the line r  b  a  b 1) 3a 2) 2a 3) a 4) 0
can be written as r  a   b Scalar product of four vectors:
For the point of intersection of the above two lines, 8. a  2 i  3 j  k , b   i  2 j  4k ,
we have a   b  b   a      1 c  i  j  k , d  i  j  k then
 r  a  b  3i  j  k
 a  b  .  c  d   ___
W.E-3:  b  c    c  a  is equal to 1) 4 2) 24 3) 36 4) 4

  
Sol :  b  c    c  a    b  c  .a c   b  c  .c a  9. If  a  b  c  b    a . b  b . c     a . c 
then  
  a b c  c   b c c  a   a b c  c 2
2 2
1) a 2) b 3) c 4) 0

LEVEL - I (C.W) 10.  a  i  b  i    a  j  b  j  
Vector triple product:  a  k  b  k  
1. If a  i  j  k , b  i  j  k , c  2 i  3 j  k , 1) a .b 2) 3  a .b  3) 0 4) 2  a .b 
then (a  b )  c 
11. If a is parallel to b  c , then  a  b   a  c  
1) 2 i  6 j  2k 2) 6i  2 j  6k
2 2

3) 6i  2 j  6k 4) 6i  2 j  6k
1) a  b .c  2) b  a .c 
2
2. If a  i  j  k , b  i  j , c  i and 3) c  a .b  4) 0
(a  b )  c   a   b, then   
109

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller UpperCrust. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $20.89. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

67096 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$20.89
  • (0)
  Add to cart